Finite Group Databasebeta

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C23×#66873 #15617280

order2816
isoclinismisoclinic class of #4323
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#66873

Splittings

FittingC23×C11×C4⋊C4 ⋊ C2
SylowC11 ⋊ C23×#102

Subgroups

subgroupG/H
centerC25C22⋊D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC23×C11×C4⋊C4C2
socleC25×C11D4
prime radicalC24×D44C2
cosocleC2×C4×C11C25
hypercenterC23×C4⋊C4D11
hypocenterC11C23×#102
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033075);